If `f(x)=sgn(x)={(|x|)/x,x!=0, 0, x=0 and g(x)=f(f(x)),`then at `x=0,g(x)` is

If f(x)=sgn(x)" and "g(x)=x^(3) ,then prove that lim_(xto0) f(x).g(x) exists though lim_(xto0) f(x) does not exist.

Let f(x) and g(x) be two equal real function such that f(x)=(x)/(|x|) g(x), x ne 0 If g(0)=g'(0)=0 and f(x) is continuous at x=0, then f'(0) is

f(x)=x^(x),x in(0,oo) and let g(x) be inverse of f(x), then g(x) 'must be

Let g(x)=1=x-[x] and f(x)={-1, x < 0 , 0, x=0 and 1, x > 0, then for all x, f(g(x)) is equal to (i) x (ii) 1 (iii) f(x) (iv) g(x)

If f(x)=sin x and g(x)=f(f(f,.....(f(x)))) then value of g'(0)+g''(0)+g'''(0) equals

If f(x) is a quadratic expression such that f(x)gt 0 AA x in R , and if g(x)=f(x)+f'(x)+f''(x) , then prove that g(x)gt 0 AA x in R .

f(x)=x o* g(x)=[(sin pi)/(x),x!=0;0x=0 check continuity of f(x)+-g(x)

If f(x)=e^(x)g(x),g(0)=2,g'(0)=1, then f'(0) is